A CONSTRAINT ON THE ANOMALOUS GREEN’S FUNCTION

It is shown that the physical constraint of the Anomalous Green’s function gives a natural pairing condition. The resulting self-consistency equation is directly related to the BCS gap equation. Both inhomogeneous and homogeneous systems are considered to illustrate the importance of the constraint. Especially we find weak localization correction to the phonon-mediated interaction.

A NOVEL APPROACH TO DOUBLE COMMUTATORS IN CHIRAL GAUGE THEORIES CONSISTENT WITH THE JACOBI IDENTITY

We give a BJL-type prescription for calculating a double commutator which manifestly respects the Jacobi identity. This prescription is used to calculate the double commutators of currents and electric fields in chiral gauge theories, where they are known to violate the Jacobi identity in an iterative computation. We then derive a consistency equation relating the Schwinger terms of the double commutators of currents and the divergence anomaly. While this consistency equation is violated by the iterative scheme in four space-time dimensions, it is found to be satisfied using our prescription.